On the stability of delay-differential systems in the behavioral framework

2001 ◽  
Vol 46 (10) ◽  
pp. 1634-1638
Author(s):  
M.E. Valcher
Keyword(s):  
Differential Systems ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential

scholarly journals Exponential Stability of Impulsive Stochastic Delay Differential Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaotai Wu ◽  
Litan Yan ◽  
Wenbing Zhang ◽  
Liang Chen
Keyword(s):  
Exponential Stability ◽  
The Other ◽  
Stability Criteria ◽  
Differential Systems ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Average Impulsive Interval

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both thepth moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples.

scholarly journals A comparison principle and stability for large-scale impulsive delay differential systems

2005 ◽  
Vol 47 (2) ◽  
pp. 203-235 ◽  
Author(s):  
Xinzhi Liu ◽  
Xuemin Shen ◽  
Yi Zhang
Keyword(s):  
Comparison Principle ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Neutral Systems ◽  
Differential Systems ◽  
Impulsive Delay ◽  
Linear And Nonlinear ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential

AbstractThis paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.

scholarly journals Stability of linear neutral delay-differential systems

1988 ◽  
Vol 38 (3) ◽  
pp. 339-344 ◽  
Author(s):  
Li-Ming Li
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

Sufficient conditions are obtained for the stability of linear neutral delay-differential systems by using a delay-differential inequality.

scholarly journals Delay-Dependent Stability, Integrability and Boundedeness Criteria for Delay Differential Systems

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 138
Author(s):  
Osman Tunç ◽  
Cemil Tunç ◽  
Yuanheng Wang
Keyword(s):  
Multiple Time ◽  
Time Varying ◽  
Differential Systems ◽  
First Order ◽  
Uniformly Asymptotic Stability ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with non-perturbed and perturbed systems of nonlinear differential systems of first order with multiple time-varying delays. Here, for the considered systems, easily verifiable and applicable uniformly asymptotic stability, integrability, and boundedness criteria are obtained via defining an appropriate Lyapunov–Krasovskiĭ functional (LKF) and using the Lyapunov– Krasovskiĭ method (LKM). Comparisons with a former result that can be found in the literature illustrate the novelty of the stability theorem and show new contributions to the qualitative theory of solutions. A discussion of two illustrative examples and the obtained results are presented.

scholarly journals Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao ◽  
Hui Zhang
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Differential Systems ◽  
Order Linear ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Theoretical Results

We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

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